Polymers 2011, 3, 886-898; doi:10.3390/polym3020886
OPEN ACCESS

polymers
ISSN 2073-4360
www.mdpi.com/journal/polymers
Review

Brillouin Scattering in Polymer Optical Fibers: Fundamental
Properties and Potential Use in Sensors
Yosuke Mizuno * and Kentaro Nakamura
Precision and Intelligence Laboratory, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku,
Yokohama 226-8503, Japan; E-Mail: knakamur@sonic.pi.titech.ac.jp* Author to whom correspondence should be addressed; E-Mail: ymizuno@sonic.pi.titech.ac.jp;
Tel.: +81-45-924-5052; Fax: +81-45-924-5091.
Received: 15 April 2011; in revised form: 9 May 2011 / Accepted: 25 May 2011 /Published: 26 May 2011

Abstract: We review the fundamental properties of Brillouin scattering in a perfluorinatedgraded-index polymer optical fiber (PFGI-POF) with 120 m core diameter. The
experiments were performed at 1.55 m telecommunication wavelength. The Brillouinfrequency shift (BFS) and the Brillouin bandwidth were 2.83 GHz and 105 MHz,
respectively. The Brillouin gain coefficient was calculated to be 3.09 × 10−11 m/W, which
was comparable to that of fused silica fibers. The Brillouin threshold power of the 100 m
POF was estimated to be as high as 24 W, which can be, for practical applications, reduced
by using POFs with smaller cores. These properties were compared with those ofsilica-based graded-index multi-mode fibers. We also investigated the BFS dependences on
strain and temperature. They showed negative dependences with coefficients of−121.8 MHz/% and −4.09 MHz/K, respectively, which are −0.2 and −3.5 times as large as
those in silica fibers. These BFS dependences indicate that the Brillouin scattering in
PFGI-POFs can be potentially applied to high-accuracy temperature sensing with reduced
strain sensitivity.
Keywords: Brillouin scattering; polymer optical fiber; fiber-optic sensing; nonlinear optics

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1. Introduction
Compared to other standard glass fibers, polymer optical fibers (POFs) [1,2] are known to provide
extremely easy and cost-effective connection; besides, they are flexible enough to endure over 40%
strain [3]. Therefore, despite their higher loss than that of silica glass fibers, POFs have been utilized
in medium-range communication applications such as home networks and automobiles [4], and in
high-strain monitoring applications [3,5] as well. On the other hand, Brillouin scattering in opticalfibers [6,7], which is one of the most significant nonlinear processes, has been widely studied. It has
been applied to a number of useful devices and systems, such as optical amplifiers [7], lasers [7,8],
optical comb generators [8], microwave signal processors [9], slow light generators [10], phaseconjugators [11], tunable delay lines [12], and strain/temperature sensors [13-15]. Up to now, Brillouinscattering has been studied not merely for silica fibers but for some specialty fibers including tellurite
glass fibers [16,17], As2Se3 chalcogenide fibers [18,19], bismuth-oxide highly-nonlinear fibers [20,21],and photonic crystal fibers [22,23]. However, Brillouin scattering in POFs has not yet been observed
and reported, which will add a variety of advantages of POFs to the conventional application field of
Brillouin scattering.
In this review, we summarize the fundamental properties of Brillouin scattering in a POF in the
1.55 m wavelength region [24]. The Brillouin frequency shift (BFS) of 2.83 GHz and the Brillouin
linewidth of 105 MHz are measured. The calculated Brillouin gain coefficient gB of 3.09 × 10−11 m/W
is close to that of fused silica fibers. The Brillouin threshold power is estimated to be as high as 24 W,
which is in agreement with the theoretical predictions reported so far. These properties were comparedwith those of silica-based graded-index multi-mode fibers. For sensing applications, we also
summarize the strain- and temperature-dependences of the BFS in the POF [25]. The BFS in the
POF moves toward lower frequency with increasing strain and temperature with coefficients of–121.8 MHz/% and –4.09 MHz/K, respectively. Compared to the coefficients of +580 MHz/% and+1.18 MHz/K in silica fibers, their absolute values are 0.2 and 3.5 times as large, respectively. TheseBFS dependences seem to be caused by the dependences of the Young’s modulus on strain andtemperature in the POF. We believe Brillouin scattering in POFs can be potentially used to implement
high-accuracy temperature sensors with low strain sensitivity.
2. Brillouin Scattering in Optical Fibers [7]When a light beam is injected into an optical fiber, it interacts with acoustic phonons, and generates
backscattered light called Stokes light. This phenomenon is called spontaneous Brillouin scattering.
Since the phonons decay exponentially, the backscattered Brillouin light spectrum, also known as
Brillouin gain spectrum (BGS), takes the shape of Lorentzian function with the bandwidth of several
tens of MHz. The frequency where the peak power is obtained in the BGS is down-shifted by several
GHz from the incident light frequency, and the amount of this frequency shift is known as BFS. In
optical fibers, the BFS B is given as [7]B 

2n v A

p



2n

E

p



(1)

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where n is the refractive index, vA the acoustic velocity in the fiber, p the wavelength of the incident
pump light, E the Young’s modulus, and the density. If tensile strain is applied or temperature ischanged in a standard silica single-mode optical fiber (SMF), the BFS moves to higher frequency inproportion to the applied strain (+580 MHz/%) [26] and the temperature change (+1.18 MHz/K) [27].
In some specialty fibers, such as tellurite glass fibers, it is known that the BFS moves to lower
frequency with increasing applied strain (−230 MHz/%) [17] and temperature (−1.14 MHz/K) [21]. In
both cases, we can derive the strain amplitude and temperature change by measuring the BFS in
the fiber.
3. Experiments (I): Fundamental Properties
In this section, we describe the experiments which reveal fundamental properties of Brillouinscattering in POFs, such as BFS, Brillouin linewidth, Brillouin gain coefficient, and Brillouinthreshold power [24]. We also compare these properties with those of silica-based graded-index
multimode fibers.
3.1. Experimental Setup
A standard POF composed of polymethyl methacrylate (PMMA) [1,2] is optimally designed forlight transmission at 650 nm, with a propagation loss of ~200 dB/km. However, its loss attelecommunication wavelength is so high (>>1 × 105 dB/km) that the Brillouin signal cannot be
detected. In the meantime, in order to observe Brillouin scattering in a PMMA-based POF at 650 nm,
we need to prepare all the necessary optical devices at this wavelength, which are quite difficult toprepare. Therefore, we used a 100-m perfluorinated graded-index POF (PFGI-POF) [28] instead of a
PMMA-based POF. It has a numerical aperture (NA) of 0.185, a core diameter of 120 m, a corerefractive index of 1.35, and lower loss (~150 dB/km) even at 1.55 m.
Figure 1 depicts the experimental setup for studying the Brillouin scattering properties in the
PFGI-POF. For the BGS measurement with high resolution, we employed self-heterodyne detection [15].
All the optical paths except the POF itself were composed of silica SMFs. A distributed-feedback laser
diode (DFB-LD) at 1,552 nm was employed as a light source, and its output was divided into two lightbeams with an optical coupler. One of the beams was, after passing a polarization controller (PC),directly used as the reference light of the heterodyne detection. The other beam was amplified with an
erbium-doped fiber amplifier (EDFA) and injected into the POF as the pump light. Then, the opticalbeat signal between the backscattered Stokes light and the reference light was converted to anelectrical signal with a photo-diode (PD). Finally, the signal was amplified by 23 dB with an electricalpre-amplifier, and monitored with an electrical spectrum analyzer (ESA).
We optically coupled the silica SMF and the POF using so-called butt coupling [29]. Since the core
diameters are quite different (8 m of SMF vs. 120 m of POF), large optical loss is expected whenlight travels from the POF into the SMF. However, this loss contributes only to the attenuation of the
Stokes light once generated in the POF, and it was measured to be approximately 12 dB. On the other
hand, when light travels from the SMF into the POF, the loss was less than 0.2 dB, which is low
enough to investigate the Brillouin scattering properties in the POF.

Polymers 2011, 3889

Figure 1. Experimental setup for investigating the Brillouin scattering properties in the
PFGI-POF. DFB-LD, distributed-feedback laser diode; EDFA, erbium-doped fiber
amplifier; ESA, electrical spectrum analyzer; PC, polarization controller; PD, photo-diode.

3.2. Experimental Results
The measured BGS when the 100 m PFGI-POF was pumped with 20 dBm light is shown in
Figure 2. The peak corresponding to the BFS was observed at 2.83 GHz, which is about 4 times lower
than that of standard silica fibers. This allows the use of a PD and an ESA that are cheaper with lower
bandwidth. The acoustic velocity vA can be calculated using the BFS B as Equation (1). With n of
1.35 andp of 1,552 nm, vA in this POF was calculated to be 1,627 m/s, which is much lower than thatof standard bulk PMMA, ~2,700 m/s [30]. By Lorentzian fitting, the 3 dB Brillouin linewidth B was
measured to be 105 MHz, which is 3–5 times broader than that of silica fibers [31], resulting in
deterioration of the sensitivity of time-domain sensors [13]. Here, we should bear in mind that theactual linewidth may be narrower due to the multimode nature of the PFGI-POF.
Figure 2. (a) BGS in the 100 m PFGI-POF when the pump power was 20 dBm.
(b) Magnified view around the BGS peak.

(a)

(b)

The dependence of the relative Stokes power on pump power is shown in Figure 3. The Stokes
power is generally known to grow exponentially at the Brillouin threshold power Pth and then reaches

Polymers 2011, 3

890

saturation, which indicates the transition from spontaneous to stimulated Brillouin scattering (SBS).
Although rough estimation of Pth is often performed using this kind of figure [7,16,18,31,32], thesaturation of the Stokes power was not observed in Figure 3. Therefore, Pth of this POF appears to bemuch higher than 30 dBm, i.e., 1 W. The detailed estimation of Pth will be given in Section 3.3.
Figure 3. Relative power of the Stokes light backscattered from 100 m PFGI-POF vs. pump power.

3.3. Discussions
First, we estimate the Brillouin gain coefficient gB. Using the acoustic velocity vA and the Brillouin
linewidth B, gB is given by [32]gB 

2  n7 p12 2
c  p 2  v A  B

(2)

where p12 is the longitudinal elasto-optic coefficient, and c the light velocity. Since the accurate valuesof p12 and  are not known for perfluorinated PMMA, we used the values of standard PMMA [33] inthis calculation. Using the measured values of vA = 1,627 m/s and B = 105 MHz, along withn = 1.35, p12 = 0.297, p = 1,552 nm, and = 1,187.5 kg/m3, gB was calculated to be 3.09 × 10−11 m/W,
which is close to that of silica fibers (3–5 × 10−11 m/W) [7]. Here, again, due to the multimode natureof the PFGI-POF, we should note that actual gB may be larger than this value.
Then, we estimate the Brillouin threshold power Pth of the PFGI-POF. An alternative way to
calculate gB is to use the following equation [34]:gB 

21 b Aeff
K Pth Leff(3)

where Aeff is the effective cross-sectional area, and Leff is the effective length defined as

Leff  1  exp   L  (4)Here,  is the background loss and L is the fiber length. For multimode fibers, a correction factor b isneeded [35], which can be treated as 2 when the NA is approximately 0.2. K is a constant that depends
on the polarization properties of the fiber [32,36], which is 1 if the polarization is maintained and0.667 otherwise. Then, using the values of gB = 3.09 × 10−11 m/W, b = 2 [35], Aeff = 209 m2 [37],K = 0.667,  = 0.056 /m, and L = 100 m, Pth can be calculated to be 24 W. This is quite high but valid

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compared to the theoretical values of ~10 W (L = 300 m) [37] or ~100 W (L = 100 m) [38]. Since Pth isin proportion to b‧Aeff in Equation (3), Pth can be decreased to a moderate power level by using POFs
with smaller core diameters.
3.4. Comparison with Silica-Based Graded-Index Multimode Fiber
In order to compare the obtained properties of the PFGI-POF with those of a silica-based
graded-index multimode fiber (GI-MMF), the Brillouin scattering in GI-MMF was experimentally
characterized in the same manner. The setup was the same as in Figure 1 except that the electricalpre-amplifier was not used. The GI-MMF was 100 m in length, with a core diameter of 50 m and NA
of 0.2. The connection loss of the butt coupling was less than 0.2 dB even when light travels from the
GI-MMF into the SMF.
Figure 4 shows the measured BGS at the pump power of 15, 20, and 25 dBm, from which we
obtained 10.43 GHz as the BFS B and 47 MHz as the Brillouin linewidth B. Using Equation (2)with n = 1.46, p12 = 0.286 [39], p = 1,552 nm, and = 2,200 kg/m3 [40], the Brillouin gain coefficientgB was calculated to be 1.63 × 10−11 m/W, which was of the same order as that of silica SMFs
(3–5 × 10−11 m/W) [7].
Figure 4. BGS of the 100 m GI-MMF at the pump power of 15, 20, and 25 dBm.

Figure 5 shows the dependence of the relative Stokes power on the pump power. The transition
from spontaneous to stimulated Brillouin scattering was not observed. Using Equation (3) with b = 2,
Aeff = 131 m2 [41,42], K = 0.667,  = 0.000092 /m, and L = 100 m, the Brillouin threshold power Pth
was calculated to be approximately 5 W. This value is much higher than ~0.3 W, the typical Pth of a
100 m SMF [7,32]. This is mostly due to the difference between the core diameters (50 m of MMF
vs. ~10 m of SMF), since Pth is in proportion to Aeff as shown in Equation (3). On the other hand, the5 W threshold of the GI-MMF is ~30 times lower than Pth of a 100 m step-index (SI-) MMF, which is
as high as ~160 W according to Eichler et al’s experiment [43]. We think the smaller mode dispersion
of GI-MMFs is the cause of this difference, or in other words, Pth of GI-MMFs is lower probably
because the fundamental mode is mainly excited, while multiple modes are excited in SI-MMFs.

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Figure 5. Relative Stokes power as a function of pump power in the 100 m GI-MMF.

In Table 1, the properties of the two fibers are summarized. We believe this information will be auseful guideline for developing POF-based systems in future.
Table 1. Comparison of the material properties between the PFGI-POF and the GI-MMF
used in this experiment: L, fiber length; NA, numerical aperture; d, core diameter; n,approximate refractive index of the core; Aeff, effective cross-sectional area; B, Brillouinfrequency shift; vA, acoustic velocity; B, Brillouin linewidth; gB, Brillouin gain
coefficient; Pth, Brillouin threshold power.
Aeff [mm2] B [GHz] vA [m/s] B [MHz]gB [×10−11 m/W] Pth [W]

L [m]

NA

d [mm]nPFGI-POF

100

0.185

120

1.35

209

2.83

1,627

105

3.09

24

GI-MMF

100

0.2

50

1.46

131

10.43

5,544

47

1.63

5

4. Experiments (II): Potential Use in Sensors
In this section, we describe the experiments for investigating the strain- and temperature-dependencesof the BFS in the PFGI-POF, and clarify that Brillouin scattering in PFGI-POFs can be potentially
utilized to develop high-accuracy temperature sensors with reduced strain sensitivity [25]. We also
show that these BFS dependences are probably caused by the dependences of the Young’s modulus on
strain and temperature in the PFGI-POF.
4.1. Experimental Setup
We used a short PFGI-POF (5 m) with the same physical properties as that used in the previous
experiments. The experimental setup for investigating the BFS dependence on strain and temperaturein the PFGI-POF is basically the same as that shown in Figure 1. The Brillouin signal generated in the
1 m SMF between the circulator and the PFGI-POF is included in the Stokes light, but it has noinfluence on the BGS measurement, because the BFS in the SMF is typically 11 GHz, about 4 times
higher than that in the PFGI-POF. The whole length of the PFGI-POF was fixed on a translation stage
using epoxy glue, to which different strains were applied. Temperature was adjusted with a heater
along the whole length of the PFGI-POF.

Polymers 2011, 3893

4.2. Experimental Results
Figure 6(a) shows the strain-dependence of the BGS in the PFGI-POF. The pump power was
19 dBm, and strains of 0.2, 0.4, 0.6, 0.8 and 1.0% were applied. As the applied strain increased, the
BGS shifted toward lower frequency. Figure 6(b) shows the strain-dependence of the BFS. The slope
was almost linear, and its coefficient was −121.8 MHz/%. While the negative sign is the same as intellurite glass fibers [17], the absolute value was approximately one fifth of that of a standard silica
SMF (+580 MHz/%) [26].
Figure 6. (a) BGS dependence on strain in the PFGI-POF. (b) BFS as a function of applied strain.

(a)

(b)

Then, Figure 7(a) shows the temperature-dependence of the BGS in the PFGI-POF. The pump
power was 23 dBm, and the temperature was controlled from 30 °C up to 80 °C with a step of 10 °C.
As temperature increased, the BGS also shifted toward lower frequency. The Stokes power at hightemperature over 40 °C was lower than that at 30 °C by about 0.7 dB probably because of the nonuniform
temperature distribution on the heater. Figure 7(b) shows the temperature-dependence of the BFS, and its
coefficient was −4.09 MHz/K. Though the negative sign is also the same as in tellurite glass fibers [21],the absolute value was about 3.5 times as large as that of an SMF (+1.18 MHz/K) [27].
Figure 7. (a) BGS dependence on temperature in the PFGI-POF. (b) BFS as a function of temperature.

(a)

(b)

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The larger temperature coefficient leads to accuracy enhancement of the temperature measurement.
On the other hand, the smaller strain coefficient means that PFGI-POF-based Brillouin sensors are lesssusceptible to the applied strain. Therefore, the Brillouin scattering in the PFGI-POF can be potentially
utilized to implement high-accuracy temperature sensors with low strain sensitivity.
4.3. Discussions
The origins of the BFS dependences on strain and temperature in the PFGI-POF are discussed. The
strain coefficient of the normalized BFS is given, by differentiating Equation (1) with respect tostrain, as:

1  B 1 n 1 E  1   
 B  n  2 E   2   (5)here the following two equations hold true [26]:p    p11  p12 1 n
 n 2 12
n 
2

(6)

1  1  2

 
2

(7)



where p11 and p12 are the elasto-optic coefficients, and  is the Poisson’s ratio. As their values in
PFGI-POF are unknown, we used the values for bulk PMMA: p11 = 0.3 [44], p12 = 0.297 [44], and = 0.34 [45]. Then the first and the third terms in Equation (5) were calculated to be –0.0857 and+0.16, respectively. Though the second term is reported to drastically vary depending both on themethod to apply strain and on the fabrication quality of the fiber, we used −5.75 as the second term,
which is the value reported in [46] for a standard PMMA-based POF. Compared to its absolute value,
the first and the third terms are negligibly small. Then the theoretical strain coefficient was calculated
to be −160.6 MHz/%. Considering that each term in Equation (5) was estimated using the values of
PMMA, this value is in moderate agreement with the experimental value of −121.8 MHz/%. Thus, thestrain-dependence of the BFS appears to originate from the dependence of the Young’s modulus on
strain in the PFGI-POF.
Next, we discuss the BFS dependence on temperature in the same manner. The temperature
coefficient of the normalized BFS is expressed as

1  B 1 n 1 E  1   
 B T n T 2E T  2  T (8)

the first term can be calculated to be −0.0000889 referring to the value reported for a standard
PMMA-based POF [33]. In order to estimate the second and the third terms, we plotted the Young’s
modulus and the density of bulk PMMA at various temperatures using the data in [47], as shown in
Figure 8(a,b). Using their slopes (–0.0295 GPa/K and −0.409 kg/m3/K), along with E ~ 6 GPa and= 1,187.5 kg/m3, the second and the third terms were calculated to be −0.00246 and +0.000172,
respectively. Then the theoretical temperature coefficient was calculated to be −6.72 MHz/K, which isin rough agreement with the experimental value of −4.09 MHz/K. Thus, the temperature-dependencePolymers 2011, 3895

of the BFS also seems to originate from the large negative dependence of the Young’s modulus ontemperature in the PFGI-POF.
Figure 8. (a) Young’s modulus of bulk PMMA vs. temperature. (b) Density of bulk
PMMA vs. temperature (plotted using the data reported in [47]).

(a)

(b)

5. Conclusions
We made a review on the Brillouin scattering properties in the PFGI-POF at 1.55 m wavelength.
The BFS and the Brillouin linewidth were 2.83 GHz and 105 MHz, respectively. Using these values,
the Brillouin gain coefficient was calculated to be 3.09 × 10−11 m/W, which is almost the same as thatof standard silica SMFs and higher than that of silica GI-MMFs. Here, we should bear in mind theactual Brillouin linewidth and the actual Brillouin gain coefficient may be narrower and higher,
respectively, than these values due to the multimode nature of the PFGI-POF. This fact indicates that,
as Brillouin scattering in silica fibers has wide application fields, Brillouin scattering in POFs can also
be utilized to develop a number of medium-range practical devices and systems with their low cost,ease of installation, high flexibility, and high safety.
We also summarized the BFS dependences on strain and temperature in a 5 m PFGI-POF. They
showed negative dependences with coefficients of −121.8 MHz/% and −4.09 MHz/K, respectively,
which are −0.2 and −3.5 times as large as those in silica fibers. These BFS dependences were found to
originate from the dependences of the Young’s modulus on strain and temperature. Thus, Brillouinscattering in PFGI-POFs has a big potential for high-accuracy temperature sensing with reduced
strain sensitivity.
For the implementation of such sensing systems, the most important problem to be solved is theextremely low power of the Stokes light, which is associated with the Brillouin threshold power of as
high as 24 W. In other words, low signal-to-noise ratio (SNR) is the major disadvantage of currently
feasible Brillouin-based distributed POF sensors as compared to Rayleigh-based POF sensors [5]. As
discussed in Section 3.3, one way to enhance the Brillouin signal is to employ POFs with smaller core
diameters. Another method is to observe SBS, not spontaneous scattering, based on so-called
pump-probe technique [48]. We expect further research will extend the potential of Brillouin scatteringin POFs not only for novel sensors but also for other useful devices and systems.

Polymers 2011, 3896

Acknowledgements
We are indebted to Nishiyama and Uenohara of Tokyo Institute of Technology, Japan, for lending
us their high-power EDFAs. Y. Mizuno is grateful to the Research Fellowships for Young Scientists
from the Japan Society for the Promotion of Science (JSPS).
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